Page 1 of 17EXAMPLE: Can we predict your final grade in the class from your 1st exam score?Regression Analysis: Grade versus Exam1 The regression equation isGrade = 36.8 + 0.614 Exam1 Predictor Coef SE Coef T PConstant 36.832 1.655 22.26 0.000Exam1 0.61352 0.02060 29.78 0.000S = 5.76575 R-Sq=67.1% R-sq(adj)=67.1%Analysis of VarianceSource DF SS MS F PRegression 1 29480 29480 886.77 0.000Residual Error 434 14428 33Total 435 43908Unusual ObservationsObs Exam1 Grade Fit SE Fit Residual St Resid 1 72 57.250 81.005 0.313 -23.755 -4.13R 2 42 58.000 62.600 0.814 -4.600 -0.81 X 4 72 60.313 81.005 0.313 -20.693 -3.59R 5 51 34.813 68.121 0.643 -33.309 -5.81R 6 36 53.720 58.919 0.932 -5.199 -0.91 X 7 63 60.000 75.484 0.433 -15.484 -2.69R 10 54 57.750 69.962 0.588 -12.212 -2.13R 13 48 57.500 66.281 0.699 -8.781 -1.53 X 15 75 67.500 82.846 0.289 -15.346 -2.66R 24 81 69.000 86.527 0.279 -17.527 -3.04R 33 45 65.250 64.440 0.756 0.810 0.14 X 39 78 72.750 84.686 0.277 -11.936 -2.07REtc….R denotes an observation with a large standardized residual.X denotes an observation whose X value gives it large leverage.Predicted Values for New ObservationsNewObs Exam1 Fit SE Fit 95% CI 95% PI 1 80.0 85.913 0.277 (85.370, 86.457) (74.568, 97.259)200-20-4099.99990501010.1ResidualPercent10090807060200-20-40Fitted ValueResidual22.515.07.50.0-7.5-15.0-22.5-30.01007550250ResidualFrequency400350300250200150100501200-20-40Observation OrderResidualNormal Probability Plot Versus FitsHistogram Versus OrderResidual Plots for Grade1101009080706050403011010090807060504030Exam1GradeScatterplot of Grade vs Exam1Page 2 of 17EXAMPLE – What is the relationship between height and weight for UF students?Data on UF students’ heights and weights collected by STA3024 students. N=1309Questions about some data – are these heights correct?HT WTF 50.0 111F 51.0 115F 51.0 95F 52.0 113F 53.0 118F 53.0 120F 53.0 120F 53.0 130F 54.0 117F 54.0 130F 55.0 121F 55.0 128F 56.0 120F 56.0 122F 56.0 128F 57.0 103F 57.0 116F 57.0 140M 57.0 165F 58.0 104F 58.0 130F 58.0 90F 58.0 92F 58.0 95F 59.0 104F 59.0 110F 59.0 115F 59.0 125F 59.0 96F 59.0 97F 59.5 145M 80 160M 83 227M 83 227M 84 255M 89 296M 72 60M 73 105F 64 270908070605030025020015010050HTWTScatterplot of WT vs HTPage 3 of 17Regression Analysis: WT versus HT The regression equation isWT = - 279 + 6.41 HTPredictor Coef SE Coef T PConstant -279.01 11.19 -24.92 0.000HT 6.4088 0.1649 38.86 0.000S = 24.2205 R-Sq = 54.2% R-Sq(adj) = 54.2%Analysis of VarianceSource DF SS MS F PRegression 1 885986 885986 1510.29 0.000Residual Error 1276 748543 587Total 1277 1634529Predicted Values for New ObservationsNewObs HT Fit SE Fit 95% CI 95% PI 1 65 137.562 0.816 (135.961, 139.163) (90.019, 185.106) 2 60 105.518 1.448 (102.678, 108.359) (57.917, 153.120) 3 76 208.059 1.519 (205.080, 211.038) (160.449, 255.669) 8075706560300250200150100HTWTS 24.2205R-Sq 54.2%R-Sq(adj) 54.2%Fitted Line PlotWT = - 279.0 + 6.409 HT100500-50-10099.999990501010.01ResidualPercent24020016012080150100500-50Fitted ValueResidual1251007550250-25-501209060300ResidualFrequency1200110010009008007006005004003002001001150100500-50Observation OrderResidualNormal Probability Plot Versus FitsHistogram Versus OrderResidual Plots for WTPage 4 of 17Regression Analysis: WT_F versus HT_F The regression equation isWT_F = - 125 + 3.96 HT_FPredictor Coef SE Coef T PConstant -125.21 17.53 -7.14 0.000HT_F 3.9614 0.2700 14.67 0.000S = 19.1292 R-Sq = 24.9% R-Sq(adj) = 24.8%Analysis of VarianceSource DF SS MS F PRegression 1 78781 78781 215.29 0.000Residual Error 650 237852 366Total 651 316633 Regression Analysis: WT_M versus HT_M The regression equation isWT_M = - 184 + 5.14 HT_MPredictor Coef SE Coef T PConstant -184.21 25.73 -7.16 0.000HT_M 5.1421 0.3633 14.16 0.000S = 26.5446 R-Sq = 24.3% R-Sq(adj) = 24.2%Analysis of VarianceSource DF SS MS F PRegression 1 141187 141187 200.37 0.000Residual Error 624 439681 705Total 625 580868 Regression Analysis: WT versus HT, GENDER_M_1 The regression equation isWT = - 165 + 4.57 HT + 21.0 GENDER_M_1Predictor Coef SE Coef T PConstant -164.68 14.76 -11.16 0.000HT 4.5699 0.2271 20.12 0.000GENDER_M_1 20.963 1.866 11.23 0.000S = 23.1134 R-Sq = 58.3% R-Sq(adj) = 58.3%Analysis of VarianceSource DF SS MS F PRegression 2 953389 476695 892.31 0.000Residual Error 1275 681140 534Total 1277 1634529Page 5 of 17Regression Analysis: WT versus HT, GENDER_M_1, HT*GENDER_M_1 The regression equation isWT = - 128 + 4.00 HT - 56.2 GENDER_M_1 + 1.14 HT*GENDER_M_1Predictor Coef SE Coef T PConstant -128.05 21.21 -6.04 0.000HT 4.0039 0.3266 12.26 0.000GENDER_M_1 -56.16 30.83 -1.82 0.069HT*GENDER_M_1 1.1382 0.4544 2.50 0.012S = 23.0840 R-Sq = 58.6% R-Sq(adj) = 58.5%Analysis of VarianceSource DF SS MS F PRegression 3 960396 320132 600.77 0.000Residual Error 1274 678879 533Total 1277 1639274Question: What if we coded gender the other way?Regression Analysis: WT versus HT, GENDER_F_1 The regression equation isWT = - 144 + 4.57 HT - 21.0 GENDER_F_1Regression Analysis: WT versus HT, GENDER_F_1, HT*GENDER_F_1 The regression equation isWT = - 184 + 5.14 HT + 56.2 GENDER_F_1 - 1.14 HT*GENDER_F_1Page 6 of 17EXAMPLE: Quadratic RegressionThe regression equation isy = - 14.0 + 3.24 x - 0.0283 x**2Predictor Coef SE Coef T PConstant -14.00 30.18 -0.46 0.659x 3.236 2.763 1.17 0.286x**2 -0.02829 0.05882 -0.48 0.648S = 8.80513 R-Sq = 79.2% R-Sq(adj) = 72.2%Analysis of VarianceSource DF SS MS F PRegression 2 1769.71 884.85 11.41 0.009Residual Error 6 465.18